GENERALIZATION OF K-THEORY FOR TURBULENT-DIFFUSION .2. SPECTRAL DIFFUSIVITY MODEL FOR PLUME DISPERSION

Further development of the spectral turbulent diffusivity concept is presented with the aim of obtaining an Eulerian dispersion model applicable for multiple interacting sources. The theory is applied for studies of plume dispersion in a field of a homogeneous and stationary turbulence. It is shown that the rate of growth and the center-line concentration obtained by the spectral diffusivity model are in agreement with results predicted by the Lagrangian statistical theory. For a narrow plume, it is shown that the plume width is proportional to the time of travel, while for a narrow puff, the 3/2-power dependence is found. For a narrow distribution, the concentration shape deviates, however, from a Gaussian shape, in contradiction to results of the statistical theory. It is shown that only two external parameters are required in the spectral turbulent diffusivity model. These are the long-wave range diffusivity coefficient K//0 and the wave vector k//m of the most energetic turbulent eddies. An Eulerian integro-differential transport equation is the final result of the model. This equation can also be used for dispersion in case of space- and time-dependent parameters. A procedure for a direct experimental test of the spectral turbulent diffusivity concept is suggested.